You can put some thinset mortar on it up to 1/4" thick, let it harden, then put on the tile. Regular thinset shouldn't be greater than 1/4" in a single layer (although you can layer it if you let it set inbetween). The tub should have a tile flange on it, if it doesn't , you may need to do some other things to make sure you don't have a moisture problem. The backerboard (this is cement backer board he put up?) should not come all the way to the top of the tub - there should be a small gap.
I suggest you ask your questions over on www.johnbridge.com you'll get more info on tiling there. Some of the same people frequent this place, but that is specifically on tiling.